Subgroup contained in the Wielandt subgroup

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Definition

A subgroup contained in the Wielandt subgroup is a subgroup of a group satisfying the following equivalent conditions:

1. It is in the Wielandt subgroup.
2. It normalizes every subnormal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup of Wielandt subgroup

Weaker properties

• Subnormal-permutable subgroup